How do you simplify #(sqrt2-3)(sqrt2+3) #?

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Answer 1 · 2016-05-29T13:59:25

Distribute the one expression over the other, then add the resulting terms together, to get to #-7#

Let's start with the original expression:

#(sqrt2-3)(sqrt2+3)#

Now let's distribute the one over the other. I'll list the answers below:

#sqrt2*sqrt2=2#
#sqrt2*3=3sqrt2#
#-3*sqrt2=-3sqrt2#
#-3*3=-9#

We can now add them up:

#2+3sqrt2-3sqrt2-9#

The square root terms subtract against each other and so drop off. We're left with #2-9=-7#